The invention pertains to a method and apparatus for controlling charged particles, and more particularly to a method and apparatus for confining ionized gases or plasmas.
Confinement of dense ionized gases is a necessary step in several processes which are currently the object of intense research. These processes include nuclear fusion. Research on the confinement and heating of ionized gases and of their electron and ionic charged particle gaseous components has concentrated principally on the methods of inertial confinement and magnetic confinement.
An example of non-magnetic and non-electric inertial confinement is the so-called "laser-fusion" process in which large pressures are to be induced over the surface of small spheres of material which it is desired to heat and confine by the vaporization and "blowoff" of surface material by laser light energy heating thereof. Such high pressures cause the compression and resulting compressional heating of the material within the small spheres. The principal difficulty of achieving useful fusion-reaction-producing conditions by such hydrodynamic-inertial confinement means is that of the lack of stability of compression, to the very high densities required, of small amounts of material in spherical or other convergent geometries. In such inertial-compression schemes it is necessary to create the forces and drive the compression sufficiently rapidly that radiation and electron conduction energy loss processes from the compressing plasma/material do not radiate and/or carry away the material internal energy before the desired particle energy (i.e., temperature) has been achieved. Typically, time scales of fractions of microseconds are required for such systems.
Attainable compression temperatures are limited by deviations from perfect symmetry of compression which lead to non-spherical compressed geometries, mixing of material, and other effects. Because of these requirements and physical difficulties such inertial-mechanical means for confining and heating plasma material have been shown to require large power input to the devices and machinery used for studies of such processes. This approach is of little interest in connection with and has no fundamental relevance to the present invention, and will not be further considered.
In magnetic confinement methods, strong magnetic fields are used in various geometries in attempts to confine or hold plasmas in well-defined spatial regions for periods of time long enough to allow their heating to desired levels of plasma ion particle energy or temperature.
An example of a device which employs a magnetic confinement method is the tokamak. The tokamak has a toroidal magnetic confinement geometry in which plasma ions and electrons are to be held within a toroidal volume by the magnetic field lines which circle through that volume.
Another example of such a device is a mirror machine. A mirror machine uses a "mirror" geometry in which opposing (facing) magnet coils act to provide a high-field surface around a central volume at lower field strength. Use of similarly-directed currents in such end coils causes "end-plugging" of a solenoidal field configuration, while oppositely-directed currents give rise to a bi-conic mirror geometry around a region in which the central magnetic field strength can drop to zero. This latter arrangement is described in more detail below.
Charged particles (e.g., plasma ions and/or electrons) gyrate around (normal to) the magnetic field lines in all such systems, in orbits whose gyro radii are set by their individual particle charge, mass, and energy of motion transverse to the magnetic fields.
As just mentioned, one of the magnetic field geometries which have been studied for plasma confinement is the simple bi-conic mirror cusp geometry. Such a system is depicted in FIGS. 1A-1C. In this system two opposing coils 100 and 110 carrying oppositely-directed currents face ("mirror") each other and produce a bipolar and equatorial field "cusp" geometry. The advantage of this system is that it is (i.e., has been shown to be) inherently stable to macroscopic "collective" losses of plasma across the field. This is in contrast to the toroidal tokamak and to the solenoidal mirror geometries which are not inherently stable to such losses. Losses in the bi-conic mirror sytem are principally out through the polar end cusps one of which is labelled 130, and the belt or equatorial "ring" cusp 135 of the magnetic field geometry. Particles 140 making up plasma 120 approach point cusp 130 from a range of angles. Most are deflected due to their having a nonaxial velocity component. Some particles, however, approach the cusp along paths which permits them to escape out through the cusp.
The total loss rate through these cusp regions is determined by the "loss cone angle" and by the solid angle (in velocity space) subtended by the leakage cusp system. The loss cone angle is set by the field strength in the current-carrying coils which make the field, and the solid angle is simply the result of the geometry chosen. In the bi-conic mirror system the losses are predominantly through the equatorial cusp 135 because of its great extent entirely surrounding the plasma region.
In experimental and theoretical work aimed at using such "mirror" field systems to confine plasmas, a remedy for this defect was attempted by twisting half the field through 90.degree. (so-called "baseball" geometry), so that the cusp leakage ring is split into orthogonal half-hemispheres. This has the effect of removing equatorial plane coherence for particles able to scatter out through the equatorial field ring loss angle. However, this twisting of the field half-space does not change the basic topology of the bi-conic system and, although still macroscopically stable, the plasma will continue to be lost predominantly through the (now-bifurcated) equatorial ring cusp in the confining field.
Studies have also been made of the solenoidal mirror geometry, in which end point cusps act as "reflectors" of particles at the ends of the quasi-solenoidal field system. As previously noted, however, the solenoidal field region itself and its connection regions to the end cusps are inherently macro-unstable with respect to plasma/field interchange displacements. Thus, while the ring cusp losses of the bi-conic cusp mirror geometry have been removed, they have been replaced by new losses due to instability of the basic central field configuration. In experimental and theoretical work on such systems a partial remedy for this defect was obtained by adding current-carrying conductors between the mirror coils, parallel to the coil system axis. These parallel conductors (sometimes called "Ioffe bars", after their Soviet inventor) provide fields which yield longitudinal surface cusp geometries which are inherently stable, but which embody particle losses through the longitudinal line cusps thus formed between conductors. In addition, locally unstable regions still exist between the central longitudinal fields and the end mirror point cusps, which lead to enhanced losses.
The virtue of the simple bi-conic mirror cusp field system is that it is inherently macroscopically stable and is thus subject only to microscopic plasma loss phenomena (e.g., collisional guiding center transport). Its defect is the very large conical sector equatorial ring cusp loss region. Polar end point cusp losses can be made small in most systems of interest by use of large mirror field ratios (particle velocity-space loss cone angle is given by sin.sup.2 .theta.=[Bo/Bm], where Bo is field strength at plasma center and Bm is field strength on the mirror cusp axis). In addition, the point cusps can be used easily for injection of plasma ions and/or electrons into the central region of such a magnetic confinement geometry. A mirror system which contained only point cusps would provide an ideal stable field/confinement geometry.
Some efforts have been expended investigating other geometries for magnetic plasma confinement. One such effort is that of R. Keller and I. R. Jones, "Confinement d'un Plasma par un Systeme Polyedrique a' Courant Alternatif", Z. Naturforschg. Vol. 21 n, pp. 1085-1089 (1966). Octahedral and truncated cube sutems were explored. These are labeled 200 and 230 in FIG. 2. Keller and Jones noted that the octadedron has two symmetry axes A and B. The truncated cube system, on the other hand, has three axes of symmetry C, D, and E. Keller and Jones experimentally explored neutral plasma heating and confinement by driving alternate interlaced coil sets at a (high) frequency of 4.7 MHz. It should be noted that the two interlaced fields used in this work were of opposite type, one being solenoidal and the other opposing bi-conical; thus alternation between field sets/states caused an inversion of field direction with each half cycle. It is not clear that alternation between such states is most effective for plasma confinement or heating. However, losses are greatly reduced from those of a conventional bi-conic equatorial ring cusp system of comparable size. Stable confinement was obtained at the experimental conditions, with modest heating observed, and the presence of a "spherical wave" was noted in the plasma.
Another extreme of magnetic confinement geometry is disclosed in U.S. Pat. No. 4,233,537 to Limpaecher. Therein it is proposed to confine neutral plasmas within a cylindrically symmetric volume whose surface contains an array of 1250 alternating magnetic poles, with axial electron injection to establish a negative plasma potential. In this system, plasma is to be confined by the surface magnetic multipole fields and constrained by the cylindrical interior negative electric potential field. In all of the arrangements considered there were always macroscopically unstable regions somewhere on the surface (e.g., at the end regions of the cylindrical volume), and the electrostatic field was never suggested as the primary or sole confinement field for plasma ions.
In both magnetic and inertial-confinement approaches the plasma heating is made to occur by statistically random collisional processes, either while under growing compression conditions or (with externally-driven energetic particles) while "trapped" for a sufficient length of time in a "confining" magnetic field geometry. It would appear to be desirable, however, to provide a more direct and non-statistical non-random process for energy addition to gain energy directly by "falling" through the negative electric potential which provides their confinement.
In the tokamak (and all other magnetic confinement systems) configuration, charged particles are lost from the system (to its walls) by transport of plasma ions and electrons across the magnetic fields by microscopic inter-particle collisions (which abruptly shift the particle gyration radius "guiding center"), and by other processes in which plasma particles, ions, and electrons act collectively to yield macroscopic transport losses of "groups" of particles across the supposed "confining" magnetic fields.
Microscopic inter-particle collisions are both inevitable and necessary in plasmas in which it is desired to achieve inter-particle nuclear reactions. Thus in a plasma confinement system of interest for the attainment of nuclear fusion reactions, it is inherently necessary that plasma particles be lost from the field geometry by collisional "jumping" of the gyro centers (above). Without collisions there can be no fusion (or other nuclear) reactions; thus the attainment of conditions for fusion reactions ensures that the magnetic field can not confine the plasma, but can only constrain its (inherent) loss rate.
In short, magnetic fields can confine (without losses) only plasmas and charged particle systems in which no collisions occur between particles. Since collisions will occur if two or more particles are in a given magnetic field system, it is evident that magnetic fields can not completely confine plasmas at densities of utility for nuclear fusion (or other nuclear) reaction production; they can only inhibit their unavoidable loss rate. In such systems the particle losses therefrom constitute an energy loss which must be made up by continuous injection of power to the system, in order to keep it operating at the desired conditions of plasma density and/or temperature. Research work to date in nuclear fusion has shown that considerable losses are inherent in the use of magnetic fields for plasma confinement.
In general it has been found that conceptual magnetic confinement systems for the production of useful fusion power generation must be very large when based on low-power-consumption magnet coils of super-conducting material. Alternatively it has been found that small tokamak systems with small power input to the plasma region can be based on magnet coils of normal-conducting materals but will require very large power input to drive these coils.
Thus, all conventional magnetic approaches to the generation of fusion power are practically unable to take advantage of the natural large energy gain (G=ratio of energy output to energy input per fusion reaction) inherent in the fusion process. This "natural" gain can be as large as G=2000 for the fusion of deuterium (D or H.sub.2) and tritium (T or H.sub.3), the two heavy isotopes of hydrogen (p or H.sub.1).
Furthermore, a magnetic field can not produce a force on a charged particle unless that particle is in motion. If it is at rest with respect to the system--and therefore not attempting to leave the system--it will not feel any force in a magnetic system. It will experience a force in such a system only if it is trying to escape from (or otherwise moving in) the system. When moving, the force exerted on such a charged particle by a magnetic field is not oppositely directed to its direction of motion, it is at right angles to its direction of motion. The magnetic force on such a moving particle is thus not a "restoring" force, it is a "deflecting" force. Because of this the field is relatively ineffective in holding neutral plasmas of equal numbers of charged particles together, as in tokamaks or mirror field geometries used in fusion research. This results in large power requirements for the machinery needed/used for confinement and plasma heating in such devices constructed according to these concepts, and the energy gain (G) potentially achievable is found to be limited by practical engineering considerations to the order of G.congruent.2 to 6.
Electrostatic systems have also been explored for the confinement of plasmas. The simplest such system is that with a spherical geometry, in which a negative potential is maintained at the center of a spherical shell by an electrode (cathode) mounted at the center. Positive ions introduced into such a geometry will be forced toward (and will "fall" to) the center until their mutual Coulombic repulsive forces exactly balance the inward-directed forces on them by the applied radial fields. In this "fall" the ions will acquire particle energies equal to the electric field potential drop. In principle, such systems offer very efficient means of reaching particle energies of interest for fusion reactions (efficiency of energy addition and thus to particle "heating" by this means is nearly 100%, which enables the achievement of very high gain G values). Unfortunately the ion densities which can be achieved by this means, within the limits of externally-supplied electric fields which are practically attainable, are too small to be of interest for fusion plasma reaction production at a useful level.
The absolute density of ions can be increased by the addition of electrons to such a system, to yield a (net) neutral plasma whose ion and electron densities are grossly equal. However, it can be shown (Earnshaw's theorem) that a (neutral) plasma can not be confined by an electrostatic field of this type. This is because the plasma ions and electrons will be subject to oppositely-directed forces in the static field and will separate, thus producing a local field gradient (due to their charge separation) which exactly cancels the applied field. In this condition the plasma can move across the field as fast as electrons are lost from its outer boundary. The speed of motion of electrons escaping from such a system is limited to that of ion motion, as the two oppositely-charged particles are tied together by their dielectric field. In a system with a static centrally-negative spherical electric field configuration, as described above, there is no force field to inhibit electron loss from the outer boundary or periphery of such a neutral plasma.
Previous workers have recognized the value of electrostatic forces for plasma/ion confinement. The earliest work was reported by William C. Elmore, James L. Tuck, and Kenneth M. Watson, "On the Inertial-Electrostatic Confinement of a Plasma", Phys. Fluids, Vol. 2, No. 3, pp. 239-246 (May-June 1959). Elmore et al proposed to overcome the difficulty of the Earnshaw's theorem limit (mentioned above) through the generation of the desired spherical radial field by the injection of energetic electrons in a radially-inward direction. This is depicted in FIG. 3. In this pioneering work electrons were to be emitted from the inner surface of a spherical shell 300 through a (screen) grid 310 at high positive potential (100 kev). Electrons so injected would pass through the grid and converge radially to a central region 330 where their electrostatic potential at the sphere center was equal to the grid injection energy. This large negative electrostatic potential, maintained by continuous electron injection (to make up losses) could then be used to trap positive ions in the system. Ions "dropped" into such a potential well would acquire energy at the "bottom" of the well (i.e., at the sphere center) equal to the negative potential established by the electron injection energy. This scheme obviously depends on the conversion of kinetic energy of injected electrons to negative electric potential fields and is thus an inertial-electrostatic method of plasma confinement. No means were provided to inhibit electron loss at the sphere surface.
Somewhat later it was shown that such a negative potential well system is unstable to various perturbations if the confined ion density exceeds a certain level. H. P. Furth, "Prevalent Instability of Nonthermal Plasma", Phys. Fluids, Vol. 6, No. 1, pp. 48-53 (January 1963). This level was shown to be so low that the system was not of practical interest. Furth agreed with Elmore et al that the system would be unstable, and further showed that such self-confined inertial electron/ion systems using electrostatic confinement were inherently unstable. That is, systems in which confining non-equilibrium electrostatic fields are to be produced by inertial-electrostatic conversion of one charged component would be unstable above some critical density of the other component. For confinement by electron injection the ion density limit is too small to be of interest.
Another system for electrostatic confinement of plasmas is set forth in U.S. Pat. Nos. 3,258,402 (June 28, 1966) and 3,386,883 (June 4, 1968) to P. T. Farnsworth. Following the approach further research has been conducted into the feasibility of electrostatic confinement of ions. See, e.g, Robert L. Hirsch, "Inertial-Electrostatic Confinement of Ionized Fusion Gases", Jour. Appl. Phys, Vol. 38, No. 11 (October 1967). Hirsch also utilized conversion of inertial energy for the production of central electrostatic fields. His work followed along the lines developed by Farnsworth (above), and utilized spherical grid structures and geometries as outlined in his U.S. Pat. Nos. 3,530,036 and 3,530,497 (both Sept. 22, 1970). Hirsch used injected ions (of D and T) rather than electrons. The several-thousand-fold mass difference (ions heavier than electrons) allowed the attainment of much more stable field/ion structures than predicted for electron injection, and the devices tested by Hirsch achieved fusion reaction rates in excess of 1.0E10 reactions/second on a continuous basis.
However, the geometry which was used was not completely spherical; the ions were injected by six opposing ion guns mounted in opposite cubic-faced array. Later analysis suggests that this geometry as well as other conditions of the experiment caused intersecting beam phenomena and ion/gas collisions to dominate over other phenomenologies important to electrostatic confinement, as these were envisioned by Farnsworth and Hirsch in their earlier work. D. C. Baxter and G. W. Stuart, "The Effect of Charge Exchange and Ionization in Electrostatic Confinement Devices", Jour. Appl. Phys., Vol. 53, No. 7, pp. 4597-4601 (July 1982). In particular, it appears that current amplification by multiple transits across the potential cavity did occur, with consequent beam buildup, in part due to reflection of ions by the grid structures opposing their own injector structures, as indicated by the sensitivity of neutron output to injection beam alignment. Here (as in the work of Elmore et al) no mechanism was invoked to provide any other confinement of electrons at the surface or periphery of the approximately-spherical system geometry.
The use of electron injection to produce negative plasma potentials for enhanced confinement in magnetic systems was examined in Soviet work on magnetic mirror systems. Work of the Soviet group at Kharkov, as reported in the Annals of the New York Academy of Sciences, Vol. 251, the proceedings of a conference held Mar. 5-7, 1974 on Electrostatic and Electromagnetic Confinement of Plasmas and the Phenomenology of Relativistic Electron Beams, (L. C. Marshall and H. L. Sahlin, ed., 1975). See, for example, Levrent'ev "Electrostatic and electromagnetic High-Temperature Plasma Traps" and also Dolan "Electric-Magnetic Confinement". These systems used physical ring electrodes in the ring cusp region of bi-conic cusp systems to inhibit plasma ion losses, and employed axial electron injection in cylindrical geometry to enhance ion magnetic confinement by producing negative potentials in the plasma region of this and of solenoidal Ioffe-bar-type mirror systems. Similar work by Blondin and Dolan invoked fixed cusp-region anode and cathode structures to aid magnetic cusp/miror plasma ion confinement by the imposition of electrostatic fields in both the polar and equatorial loss cones. D. C. Blondin and T. J. Dolan, " Equilbrium Plasma Conditions in Electrostatically Plugged Cusps and Mirrors", J. Appl. Phys., Vol. 47, No. 7, pp. 2903-2906 (July 1976). R. L. Hirsch had earlier studied this method to aid confinement in solenoidal mirror magnetic confinement systems. U.S. Pat. No. 3,655,508 (Apr. 11, 1972). Still other work utilized ion injection to establish positive potential fields in bi-conic or mirror cusp geometries, or in twisted bi-conic mirrors used as "plugs" at the ends of linear solenoids (See, e.g., F. L. Hinton and M. N. Rosenbluth, "Stabilization of Axisymmetric Mirror Plasmas by Energetic Ion Injection", Nucl. Fus., Vol. 22, No. 12, pp. 1547-1557 (1982), and P. J. Catto and J. B. Taylor, "Electrostatic Enhancement of Mirror Confinement", Nucl. Fus., Vol. 24, No. 2, pp 229-233 (1984).) All of these approaches used fixed electrodes and/or ion or electron injection to establish electric potentials to aid magnetic plasma confinement systems, not for the direct electrostatic confinement of ions.
In summary, previous work in inertial, magnetic, and electrostatic confinement aimed at the confinement of charged particles (ions), for the purpose of creating conditions useful for the generation of nuclear fusion reactions between them, has shown that:
(1) Magnetic fields do not provide restoring forces to charged particles in motion, or to confine plasma particles; they provide deflecting forces, at righ angles to the direction of motion of the particles. Electrostatic, electrodynamic, and other electric fields can provide direct restoring forces for the confinement of charged particles.
(2) Even the most favorable magnetic confinement geometries lose charged particles by gyro guiding center shifting due to microscopic collisions between particles. Such collisions are essential for the creation of nuclear reactions.
(3) Collisions between particles of like sign have the most effect on ion losses. Such collisional losses are governed by the gyro radii of ion/ion collisions in conventional magnetic confinement schemes. Electron gyro radii are very much less than those of ions of comparable energy.
(4) Electron and ion motions in magnetic fields are of opposite sign. This results in the electric polarization of the plasma, with the establishment of an ambipolar dielectric field. Plasma losses are then set by the rate of ion/ion transport collisions across the field.
(5) Inertial-electrostatic potential wells estblished and maintained by charged particle injection alone and held solely within electric field structures are stable only for confinement at particle densities below a certain critical value. This is found to be too low for the production of nuclear fusion reaction rates useful for power generation.